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At least 847 records · Page 47

Final technical report

This final report covers the final year of the project. Reports from previous years were included in the group report for that year. The objective of this part of the project was to compare results from two large-scale, nonlinear plasma simulation codes based on magnetohydrodynamics, M3D and M3D-C1, for plasma edge instabilities. This is a difficult undertaking and the comparison was only partially successful because, while the MHD equations are standard, there are a number of valid MHD models of the plasma dissipation that make different approximations to their physics and the numerical implementation of a given model can be quite different depending on the way that the rest of the equations are solved. Large differences arise, and have major effects on the predicted plasma behavior, in the case of the greatest interest to this project, the plasma edge region under conditions where the plasma edge instabilities are strongest and the background plasma changes abruptly from interior hot, dense conditions to an unconfined, cool, diffuse plasma outside the magnetic boundary surface. Experimental observations only partially measure the background plasma and there are many non-MHD processes that can have important effects (studied in the rest of the project). Comparisons for edge instabilities at very small amplitude, the so-called linear modes, had showed good agreement for a few interior plasma instabilities, but strong differences between the default models for the plasma edge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Improved CdTe PLR Estimates: Self-Shading and Spectral Mismatch

The RdTools year-on-year method of estimating performance loss rate (PLR) employs a simple normalization to remove the confounding effect of irradiance and temperature variation. However, the normalization's assumption that PV production scales linearly with in-plane broadband irradiance is a worse approximation for CdTe and other technologies with larger spectral sensitivities than it is for the more common c-Si technology. Additionally, CdTe systems using single-axis trackers (-20% of installed US utility-scale capacity) are subject to self-shading in the morning and afternoon, introducing another nonlinearity between PV output and broadband irradiance. Ignoring these effects may subject the estimated PLR to increased uncertainty, and perhaps bias, depending on the character of their short- and long-term variability. In this work we show that including self-shading and spectral mismatch models in the normalization for tracking CdTe systems can result not only in tighter PLR confidence intervals but different median PLRs as well. The shading and spectral models are kept simple to maintain consistency with the RdTools ethos of not requiring detailed system metadata or unusual measurements.

CdTe↗

X-ray diffraction at the National Ignition Facility

We report details of an experimental platform implemented at the National Ignition Facility to obtain in situ powder diffraction data from solids dynamically compressed to extreme pressures. Thin samples are sandwiched between tamper layers and ramp compressed using a gradual increase in the drive-laser irradiance. Pressure history in the sample is determined using high-precision velocimetry measurements. Up to two independently timed pulses of x rays are produced at or near the time of peak pressure by laser illumination of thin metal foils. The quasi-monochromatic x-ray pulses have a mean wavelength selectable between 0.6 Å and 1.9 Å depending on the foil material. The diffracted signal is recorded on image plates with a typical 2 θ x-ray scattering angle uncertainty of about 0.2° and resolution of about 1°. Analytic expressions are reported for systematic corrections to 2 θ due to finite pinhole size and sample offset. A new variant of a nonlinear background subtraction algorithm is described, which has been used to observe diffraction lines at signal-to-background ratios as low as a few percent. Variations in system response over the detector area are compensated in order to obtain accurate line intensities; this system response calculation includes a new analytic approximation for image-plate sensitivity as a function of photon energy and incident angle. This experimental platform has been used up to 2 TPa (20 Mbar) to determine the crystal structure, measure the density, and evaluate the strain-induced texturing of a variety of compressed samples spanning periods 2–7 on the periodic table.

47 OTHER INSTRUMENTATION↗

Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential

In this work, we present trapped solitary wave solutions of a coupled nonlinear Schrödinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system.

97 MATHEMATICS AND COMPUTING↗

Graphene-doped polymer nanofibers for low-threshold nonlinear optical waveguiding

Graphene-doped polymer nanofibers are fabricated by taper drawing of solvated polyvinyl alcohol doped with liquid-phase exfoliated graphene flakes. Nanofibers drawn this way typically have diameters measured in hundreds of nanometers and lengths in tens of millimeters; they show excellent uniformity and surface smoothness for optical waveguiding. Owing to their tightly confined waveguiding behavior, light–matter interaction in these subwavelength-diameter nanofibers is significantly enhanced. Using approximately 1350-nm-wavelength femto-second pulses, we demonstrate saturable absorption behavior in these nanofibers with a saturation threshold down to 0.25 pJ pulse -1 (peak power ~1.3 W). Additionally, using 1064-nm-wavelength nanosecond pulses as switching light, we show all-optical modulation of a 1550-nm-wavelength signal light guided along a single nanofiber with a switching peak power of ~3.2 W.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Microwave Heating of a Liquid Stably Flowing in a Circular Channel Under the Conditions of Nonstationary Radiative-Convective Heat Transfer

A class of nonlinear problems of nonstationary radiative-convective heat transfer under the microwave action with a small penetration depth is considered in a stabilized coolant flow in a circular channel. The solutions to these problems are obtained, using asymptotic procedures at the stages of nonstationary and stationary convective heat transfer on the heat-radiating channel surface. The nonstationary and stationary stages of the solution are matched, using the 'longitudinal coordinate–time' characteristic. The approximate solutions constructed on such principles correlate reliably with the exact ones at the limiting values of the operation parameters, as well as with numerical and experimental data of other researchers. An important advantage of these solutions is that they allow the determination of the main regularities of the microwave and thermal radiation influence on convective heat transfer in a channel even before performing cumbersome calculations. It is shown that, irrespective of the heat exchange regime (nonstationary or stationary), the Nusselt number decreases and the rate of the surface temperature change increases with increase in the intensity of thermal action.

42 ENGINEERING↗

On the nonlinearity of spatial scales in extreme weather attribution statements

In the context of continuing climate change, extreme weather events are drawing increasing attention from the public and news media. A question often asked is how the likelihood of extremes might have changed by anthropogenic greenhouse-gas emissions. Answers to the question are strongly influenced by the model used, duration, spatial extent, and geographic location of the event—some of these factors often overlooked. Using output from four global climate models, we provide attribution statements characterised by a change in probability of occurrence due to anthropogenic greenhouse-gas emissions, for rainfall and temperature extremes occurring at seven discretised spatial scales and three temporal scales. An understanding of the sensitivity of attribution statements to a range of spatial and temporal scales of extremes allows for the scaling of attribution statements, rendering them relevant to other extremes having similar but non-identical characteristics. This is a procedure simple enough to approximate timely estimates of the anthropogenic contribution to the event probability. Furthermore, since real extremes do not have well-defined physical borders, scaling can help quantify uncertainty around attribution results due to uncertainty around the event definition. Results suggest that the sensitivity of attribution statements to spatial scale is similar across models and that the sensitivity of attribution statements to the model used is often greater than the sensitivity to a doubling or halving of the spatial scale of the event. The use of a range of spatial scales allows us to identify a nonlinear relationship between the spatial scale of the event studied and the attribution statement.

54 ENVIRONMENTAL SCIENCES↗

Formulation and numerical analysis of a fully-coupled dynamically deforming electromagnetic wire

Here, an electromagnetic beam model is developed for the simulation of actuated electronic textiles. The beam is solved using a nonlinear director-based kinematic description with additional temperature and electric potential fields along its length. The three fields are fully coupled by mutual dependences on the deformation, Lorenz force, back electromotive force, temperature dependent constitutive responses, and the Seebeck effect. Instead of solving Maxwell's equations in full detail, a quasistatic approximation is used to solve the electric potential in the presence of a moving material medium. The current-carrying beam approximation is used to further simplify the solution space for the potential. While this formulation alleviates the spatial and temporal discretization restrictions, the coupled problem is an index-1 semi-explicit Differential Algebraic Equation requiring special treatment. The time dependent problem is solved using different Runge-Kutta methods. Diagonally implicit Runge-Kutta methods and explicit Runge-Kutta methods using implicit solution of the electric potential problem are explored. The finite element model is implemented using the open source package FEniCS, which is able to automatically generate the linearizations of the multiphysics equations required for the implicit solutions. A model problem is constructed with which to test and analyze the physical formulation and numerical solution techniques. The time stepping methods are verified using the convergence orders of the higher-order Runge-Kutta methods. Runtime comparisons show that the explicit methods are generally more computationally efficient than the implicit schemes used for this problem. For the implicit schemes, a staggered solution is significantly faster than a monolithic solution at most time step sizes. However, at very large time steps, such as those that would be used for dynamic relaxation, the monolithic solution can be more efficient than the staggered solution.

36 MATERIALS SCIENCE↗

Test-Based Calibration of Safety Factors for Capacity Models

In this paper, a simple procedure to calibrate the safety factor of capacity models is presented. The calibration can be carried out based on any available database of experimental tests, even of limited size. The procedure aims to assess the model capability of predicting the test results and to calibrate the safety factor so that the capacity equation meets the target reliability level required by the code or sought by the calibrator. After predicting each test of the database with the capacity equation under consideration, the test-prediction pairs are checked for the property of linearity, and the relative error for the properties of homoscedasticity and normality. Once these properties are fulfilled—which may require a nonlinear transformation of the test values and/or the predictions—the closed-form equation proposed in this paper is employed to compute a target design value. The model safety factor is finally obtained by comparing such target design value with the design value obtained from the code. The paper also proposes two approximate analytical equations to compute the tolerance factor, used to attain any given fractile, as a function of the (even small) number of tests, with any assigned confidence level. A fundamental outcome of the procedure is that it yields an objective indicator of the model accuracy, measured by the standard deviation of its error, which may be regarded as a parameter useful for selecting the most reliable model among different competing ones. In the long run, the application of the proposed procedure will allow achieving a uniform reliability level throughout all capacity models used in codes and guidelines. A further advantage is that the partial safety factors so derived can be straightforwardly updated when more experiments become available. Finally, as an example, the proposed procedure is herein applied to the ACI 318 shear design capacity equation for concrete members unreinforced in shear.

42 ENGINEERING↗

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Designing stellarator coils by a modified Newton method using FOCUS

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Solitary waves in the nonlinear Dirac equation in the presence of external driving forces

In this paper, we consider the nonlinear Dirac (NLD) equation in (1 + 1) dimensions with scalar–scalar self interaction g 2 /κ + 1 (Ψ¯Ψ) κ + 1 in the presence of external forces as well as damping of the form f(x) - iμγ 0 Ψ, where both f and Ψ are two-component spinors. We develop an approximate variational approach using collective coordinates (CC) for studying the time dependent response of the solitary waves to these external forces. This approach predicts intrinsic oscillations of the solitary waves, i.e. the amplitude, width and phase all oscillate with the same frequency. The translational motion is also affected, because the soliton position oscillates around a mean trajectory. For κ = 1 we solve explicitly the CC equations of the variational approximation for slow moving solitary waves in a constant external force without damping and find reasonable agreement with solving numerically the CC equations. Finally, we then compare the results of the variational approximation with no damping with numerical simulations of the NLD equation for κ = 1, when the components of the external force are of the form f j = r j exp(–iΚx) and again find agreement if we take into account a certain linear excitation with specific wavenumber that is excited together with the intrinsic oscillations such that the momentum in a transformed NLD equation is conserved.

97 MATHEMATICS AND COMPUTING↗

Uncovering extreme nonlinear dynamics in solids through time-domain field analysis

Time-domain analysis of harmonic fields with sub-cycle resolution is now experimentally viable due to the emergence of sensitive, on-chip techniques for petahertz-scale optical-field sampling. We demonstrate how such a time-domain, field-resolved analysis uncovers the extreme nonlinear electron dynamics responsible for high-harmonic generation within solids. Time-dependent density functional theory was used to simulate harmonic generation from a solid-state band-gap system driven by near- to mid-infrared waveforms. Particular attention was paid to regimes where both intraband and interband emission mechanisms play a critical role in shaping the nonlinear response. We show that a time-domain analysis of the harmonic radiation fields identifies the interplay between intra- and interband dynamical processes underlying the nonlinear light generation. With further analysis, we show that changes to the dominant emission regime can occur after only slight changes to the peak driving intensity and central driving wavelength. Furthermore, time-domain analysis of harmonic fields also reveals, for the first time, the possibility of rapid changes in the dominant emission mechanism within the temporal window of the driving pulse envelope. Finally, we examine the experimental viability of performing time-domain analysis of harmonic fields with sub-cycle resolution using realistic parameters.

74 ATOMIC AND MOLECULAR PHYSICS↗

Average nonlinear dynamics of particles in gravitational pulses: Effective Hamiltonian, secular acceleration, and gravitational susceptibility

Particles interacting with a prescribed quasimonochromatic gravitational wave (GW) exhibit secular (average) nonlinear dynamics that can be described by Hamilton’s equations. We derive the Hamiltonian of this “ponderomotive” dynamics to the second order in the GW amplitude for a general background metric. For the special case of vacuum GWs, we show that our Hamiltonian is equivalent to that of a free particle in an effective metric, which we calculate explicitly. We also show that already a linear GW pulse displaces a particle from its unperturbed trajectory by a finite distance that is independent of the GW phase and proportional to the integral of the pulse intensity.This effect is independent from the nonlinear memory effects that has been known. We calculate the particle displacement analytically and show that our result is in agreement with numerical simulations. We also show how the Hamiltonian of the nonlinear averaged dynamics naturally leads to the concept of the linear gravitational susceptibility of a particle gas with an arbitrary phase-space distribution. We calculate this susceptibility explicitly to apply it, in a follow-up paper, toward studying self-consistent GWs in inhomogeneous media within the geometrical-optics approximation

79 ASTRONOMY AND ASTROPHYSICS↗

Uncertainty propagation and sensitivity analysis for constrained optimization of nuclear waste vitrification

Abstract The vitrification of high‐level waste (HLW) by heating a mixture of glass‐forming chemicals (GFCs) with the waste can be improved using a constrained optimization problem. This study explores how different uncertainty propagation (UP) methods implemented with the optimization process can affect the glass formulation of nuclear waste glasses. UP is the effort of propagating uncertain inputs through a system to understand and quantify output distributions. Uncertainty intervals are crafted from output distributions to inform the optimization algorithm. UP is often implemented with Monte Carlo (MC) sampling for large nonlinear systems, which can be difficult to implement within a constrained optimization algorithm that requires derivative information. Other UP methods often used for optimization under uncertainty (OUU) can be designed to work within an established constrained optimization framework. Methods of UP are evaluated in this study including iterative sampling approaches, first‐order approximations, and surrogate modeling with machine learning (ML). A method of dimensional reduction based on global sensitivity analysis is introduced to support the UP methods for the large dimensionality of the problem. Analytical UP methods able to achieve similar optimums 10 times faster than the baseline MC approach, and produce 93.9% similar output distributions are reported.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

EMAPS: An Efficient Multiscale Approach to Plasma Systems with Non-MHD Scale Effects

Global interactions of energetic ions with magnetoplasmas and neutral gases lie at the core of many space and laboratory plasma phenomena ranging from solar wind entry into and transport within planetary magnetospheres and exospheres to fast-ion driven instabilities in fusion devices to astrophysics-in-lab experiments. The ability of computational models to properly account for physical effects that underlie such interactions, namely ion kinetic, ion cyclotron, Hall, collisional and ionization processes is important for the success and planning of experimental research in plasma physics. Understanding the physics of energetic ions, in particular their nonlinear resonance interactions with Alfvén waves, is central to improving the heating performance of magnetically confined plasmas for future energy generation. Fluid models are not adequate for high-beta plasmas as they cannot fully capture ion kinetic and cyclotron physics (e.g., ion behavior in the presence of magnetic nulls, shock structures, plasma interpenetration, etc.). Recent results from global reconnection simulations show that even in a MHD-like regime there may be significant differences between kinetic and MHD simulations. Therefore, kinetic modeling becomes essential for meeting modern day challenges in plasma physics. The hybrid approximation is an intermediate approximation between the fluid and fully kinetic approximations. It eliminates light waves, removes the electron inertial temporal and spatial scales from the problem and enables full-orbit ion kinetics. As a result, hybrid codes have become effective tools for exploring ion-scale driven phenomena associated with ion beams, shocks, reconnection and turbulence that control the large-scale behavior of laboratory and space magnetoplasmas. A number of numerical issues, however, make three-dimensional (3D) large-scale hybrid simulations of inhomogeneous magnetized plasmas prohibitively expensive or even impossible. To resolve these difficulties we have developed a novel Event-driven Multiscale Asynchronous Parallel Simulation (EMAPS) technology that replaces time stepping with self-adaptive update events. Local calculations are carried out only on an “as needed basis”. EMAPS (i) guarantees accurate and stable processing of physical variables in time accurate simulations, and (ii) eliminates unnecessary computation. Applying EMAPS to the hybrid model has resulted in the development of a unique parallel code, dimension-independent (compile-time-configurable) HYPERS (Hybrid Parallel Event-Resolved Simulator) that scales to hundreds of thousands of parallel processors. HYPERS advances electromagnetic fields and particles asynchronously on time scales determined by local physical laws and mesh properties. To achieve high computational accuracy in complex device geometries, HYPERS employs high-fidelity Cartesian grids with masked conductive cells. The HYPERS model includes multiple ion species, energy and momentum conserving ion-ion collisions, and provides a number of approximations for plasma resistivity and vacuum regions. Both local and periodic boundary conditions are allowed. The HYPERS solver preserves zero divergence of magnetic field. The project has demonstrated HYPERS capabilities on a number of applications of interest to fusion and astrophysical plasma physics applications listed below. 1. Theta-pinch formation of FRCs The formation, spontaneous spin-up, and stability of theta-pinch formed field-reversed configurations have been studied self-consistently in 3D. The end-to-end hybrid simulations reveal poloidal profiles of implosion-driven fast toroidal plasma rotation and demonstrate three discharge regimes as a function of experimental parameters: the decaying stable configuration, the tilt unstable configuration, and the nonlinear evolution of a fast growing tearing mode. 2. FRC collisions with magnetic mirrors Interactions of fast plasma streams and objects with magnetic obstacles (dipoles, mirrors, etc) lie at the core of many space and laboratory plasma phenomena ranging from magnetoshells and solar wind interactions with planetary magnetospheres to compact fusion plasmas. HYPERS simulations are compared with data from the MSX experiment (LANL) that focuses on the physics of magnetized collisionless shocks through the acceleration and subsequent stagnation of FRC plasmoids against a strong magnetic mirrors and flux-conserving boundaries. 3. Exploding magnetoplasmas Results from hybrid simulations of two experiments at the LAPD and Nevada Terawatt Facility are discussed where short-pulse lasers are used to ablate solid targets to produce plasmas that expand across external magnetic fields. The first simulation recreates flutelike density striations observed at the leading edge of a carbon plasma and predicts an early destruction of the magnetic cavity in agreement with experimental evidence. In the second simulation a polyethylene target is ablated into a mixture of protons and carbon ions. A mechanism is demonstrated that allows protons to penetrate the magnetic field in the form of a collimated flow. The results are compared to experimental data and single-fluid MHD simulations. The EMAPS framework has the potential for wide application in many other engineering and scientific fields, such as climate models, biological systems, electronic devices, seismic events, oil reservation simulators that all involve advancing solutions of partial differential equations in time where the rate of activity can be adapted widely over the spatial domain depending on locally space/time phenomena (“events”).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Unexpected Scaling of Peak Acceleration for a Yielding Mass-Spring System Subjected to a Triangular Base Acceleration Pulse

The use of bounding scenarios is a common practice that greatly simplifies the design and qualification of structures. However, this approach implicitly assumes that the quantities of interest increase monotonically with the input to the structure, which is not necessarily true for nonlinear structures. This paper surveys the literature for observations of nonmonotonic behavior of nonlinear systems and finds such observations in both the earthquake engineering and applied mechanics literature. Numerical simulations of a single degree-of-freedom mass-spring system with an elastic–plastic spring subjected to a triangular base acceleration pulse are then presented, and it is shown that the relative acceleration of this system scales nonmonotonically with the input magnitude in some cases. The equation of motion for this system is solved symbolically and an approximate expression for the relative acceleration is developed, which qualitatively agrees with the nonmonotonic behavior seen in the numerical results. The nonmonotonicity is investigated and found to be a result of dynamics excited by the discontinuous derivative of the base acceleration pulse, the magnitude of which scales nonmonotonically with the input magnitude due to the fact that the first yield of the spring occurs earlier as the input magnitude is increased. The relevance of this finding within the context of defining bounding scenarios is discussed, and it is recommended that modeling be used to perform a survey of the full range of possible inputs prior to defining bounding scenarios.

42 ENGINEERING↗